Question

Background This case study compares benefit/cost analysis and cost effectiveness analysis on the same information about highway lighting and its role in accident reduction. Poor highway lighting may be one reason that proportionately more traffic accidents occur at night. Traffic accidents are categorized into six types by severity and value. For example, an accident with a fatality is valued at approximately $4 million, while an accident in which there is property damage (to the car and contents) is valued at $6000. One method by which the impact of lighting is measured compares day and night accident rates for lighted and unlighted highway sections with similar characteristics. Observed reductions in accidents seemingly caused by too low lighting can be translated into either monetary estimates of the benefits B of lighting or used as the effectiveness measure E of lighting.

Information

Freeway accident data were collected in a 5-year study. The property damage category is commonly the largest based on the accident rate. The number of accidents recorded on a section of highway is presented here

	Number of Accident Recorded
	Unlighted		Lighted
Accident Type	Day	Night	Day	Night
Property damage	379	199	2069	836

The ratios of night to day accidents involving property damage for the unlighted and lighted freeway sections are 199/379 = 0.525 and 839/2069 = 0.406, respectively. These results indicate that the lighting was beneficial. To quantify the benefit, the accident rate ratio from the unlighted section will be applied to the lighted section. This will yield the number of accidents that were prevented. Thus, there would have been (2069)(0.525) = 1086 accidents instead of 839 if there had not been lights on the freeway. This is a difference of 247 accidents. At a cost of $6000 per accident, this results in a net annual benefit of

B = (247)($6000) = $1,482,000

For an effectiveness measure of number of accidents prevented, this results in E = 247. To determine the cost of the lighting, it will be assumed that the light poles are center poles 67 meters apart with 2 bulbs each. The bulb size is 400 watts, and the installation cost is $3500 per pole. Since these data were collected over 87.8 kilometers of lighted freeway, the installed cost of the lighting is (with number of poles rounded off):

Installation cost = $3500 (87.8 / 0.067) = 3500 (1310) = $4,585,000

There are a total of 87.8/0.067_1310 poles, and electricity costs $0.10 per kWh. Therefore, the annual power cost is

Annual power cost = 1310 poles (2 bulbs/pole)(0.4 kilowatt/bulb) x (12 hours/day)(365 days/year) x ($0.10/kilowatt-hour) = $459,024 per year

For an effectiveness measure of number of accidents prevented, this results in E = 247. To determine the cost of the lighting, it will be assumed that the light poles are center poles 67 meters apart with 2 bulbs each. The bulb size is 400 watts, and the installation cost is $3500 per pole. Since these data were collected over 87.8 kilometers of lighted freeway, the installed cost of the lighting is (with number of poles rounded off):

Installation cost = $3500 (87.8 / 0.067) = 3500 (1310) = $4,585,000

There are a total of 87.8/0.067_1310 poles, and electricity costs $0.10 per kWh. Therefore, the annual power cost is

Annual power cost = 1310 poles (2 bulbs/pole)(0.4 kilowatt/bulb) x (12 hours/day)(365 days/year) x ($0.10/kilowatt-hour) = $459,024 per year

The data were collected over a 5-year period. Therefore, the annualized cost C at i = 6% per year is

Total annual cost = $4,585,000( A/P ,6%,5) + 459,024 = $1,547,503

If a benefit/cost analysis is the basis for a decision on additional lighting, the B/C ratio is B/C = 1,482,000 / 1,547,503 = 0.96

The data were collected over a 5-year period. Therefore, the annualized cost C at i = 6% per year is

Total annual cost = $4,585,000( A/P ,6%,5) + 459,024 = $1,547,503

If a benefit/cost analysis is the basis for a decision on additional lighting, the B/C ratio is B/C = 1,482,000 / 1,547,503 = 0.96

Since B/C < 1.0, the lighting is not justified. Consideration of other categories of accidents is necessary to obtain a better basis for decisions. If a cost-effectiveness analysis (CEA) is applied, due to a judgment that the monetary estimates for lighting’s benefit is not accurate, the C/E ratio is

C/E = 1,547,503 / 247 = 6265

This can serve as a base ratio for comparison when an incremental CEA is performed for additional accident reduction proposals. These preliminary B/C and C/E analyses prompted the development of four lighting options:

W) Implement the plan as detailed above; light poles every 67 meters at a cost of $3500 per pole.

X) Install poles at twice the distance apart (134 meters). This is estimated to cause the accident prevention benefit to decrease by 40%.

Y) Install cheaper poles and surrounding safety guards, plus slightly lowered lumen bulbs (350 watts) at a cost of $2500 per pole; place the poles 67 meters apart. This is estimated to reduce the benefit by 25%.

Z) Install cheaper equipment for $2500 per pole with 350-watt lightbulbs and place them 134 meters apart. This plan is estimated to reduce the accident prevention measure by 50% from 247 to 124.  

Case Study Exercises Determine if a definitive decision on lighting can be determined by doing the following:

1. Use a benefit/cost analysis to compare the four alternatives to determine if any are economically justified.

2. Use a cost-effectiveness analysis to compare the four alternatives. From an understanding viewpoint, consider the following:

3. How many property-damage accidents could be prevented on the unlighted portion if it were lighted?

4. What would the lighted, night-to-day accident ratio have to be to make alternative Z economically justified by the B/C ratio?

5. Discuss the analysis approaches of B/C and C/E. Does one seem more appropriate in this type of situation than the other? Why? Can you think of other bases that might be better for decisions for public projects such as this one

please answer just 1,2 and 5... thank you very much

Answer 1